Conventional code plate systems direct light from a code plate directly onto detection gratings. Their resolution is limited by the relatively coarse rulings on the code plate and the detection gratings.
The accuracy of a code plate measuring system is determined by the absolute accuracy of the code plate itself, as well as by the precision with which the location along the code plate may be measured. Gratings are known in the art with a precision of 2 nm over dimensions up to 30 cm.
The smaller the period of the code plate and the gratings, the finer the measurements that may be made. The accuracy of determining the phase of a typical sinusoidal output measurement is typically on the order of one part per thousand, due to signal/noise and other limitations. Thus, the position of a 1 mm grating may be determined within about 1 μm, and the position of a 1 μm grating could, in principle, be determined within about 1 nm. However, such a fine pitch requires a correspondingly fine depth of focus in conventional systems, making them very difficult to use as a practical matter. In addition, previous code plate systems have generally been sensitive to factors such as variation in the distance between the code plate and the gratings, local variations in line width, and local variations in phase. Such factors have typically limited the precision of measurements made with conventional code plate systems to about 100 nm. Also, in existing code plate systems, a shadow of the code plate is typically cast upon the gratings. This method requires either a small gap between the code plate and the gratings, which is difficult to maintain as a practical matter, or it inherently degrades the resolution of the shadow cast on the gratings if a larger gap is used as a compromise measure.
Examples of prior systems using gratings for measuring position include U.S. Pat. No. 3,996,463, and published U.S. patent application 2004/0051881 A1.
Proximity Imaging. Proximity imaging uses a grating of clear and opaque lines, preferably of equal width (FIG. 1a) (a Ronchi grating). A collimated or quasi-collimated beam of light (shown schematically in FIG. 1b) casts a shadow of a first Ronchi grating onto a second Ronchi grating having the same period, and a photodetector registers the light passing through both gratings. As the first code plate moves from one position to another, the output of the photodetector passes through a series of minima and maxima. These extrema are counted to determine total movement of the code plate. To avoid possible ambiguity in the direction of motion, an optional second Ronchi grating and photodetector may be added, having a spatial phase of 90° relative to the first grating. Thus for one direction of motion a maximum in the signal from the first photodetector corresponds to a rising signal in the second photodetector, while for the other direction a maximum from the first detector corresponds to a falling signal in the second.
The sharpness of the shadow in proximity imaging is limited both by penumbral blurring and by diffraction. For a Ronchi grating of period P, the maximum permissible gap, g, is given byP/2≅√{square root over (λg)}  (1)where λ is the wavelength of the light. For example, for visible light with a wavelength of 500 nm and a gap of 50 μm, the period P must be at least about 10 microns.
Talbot Imaging. Under coherent illumination, multiple images of the grating will form, spaced at intervals of 2P2/λ (the so-called Talbot Effect). In principle, the Talbot Effect thus might allow one to use larger gaps. However, the depth of focus for each of the multiple images is still limited by equation (1). Additionally, coherent illumination is notoriously sensitive to artifacts arising from such things as dust or grating imperfections. These artifacts tend to distort Talbot images, leading to errors in the measured position of the grating. For an example of coherent distortion in a Talbot image of a grating under coherent HeNe laser light, see FIG. 2 of priority application 60/753,140 (not reproduced here).
Projection Imaging. An optical system, which may be referred to as a microscope, may be used to image a code plate onto the detection gratings, which are preferably also Ronchi gratings. Using a microscope for this purpose has the advantages of: (1) producing a large working distance to the code plate, equal to the working distance of the microscope objective, and (2) imaging onto enlarged gratings, which may be produced with relatively higher accuracy and precision than smaller gratings, and which may also be observed more readily. The depth of focus is given by
                              Depth          ⁢                                          ⁢          of          ⁢                                          ⁢          focus                =                              P            2                                2            ⁢                                                  ⁢            λ                                              (        2        )            or about 100 μm for the example conditions described above (viz., wavelength=500 nm, P=10 μm). Note from equation (2) that the depth of focus varies as the square of the period, dropping to just 1 μm for a 1 μm period grating for the same wavelength of light. This technique is not widely used, because the size of the optical system would be inconveniently large.
Spatial Filtering. Spatial filtering is sometimes used in various forms of projection imaging with coherent light. For example, zero order diffracted light from a grating may be blocked, as with a stop in a microscope objective. Spatial filtering can lead to a large depth of focus, comparable to the width of the illuminating beam. In addition, the apparent period of the grating is halved, so that, for example, the image of a 1 μm period grating appears to become that of a 0.5 μm period grating. Unfortunately, such images are subject to the same type of coherent illumination artifacts as are grating images. These artifacts may be reduced, while still preserving some of the advantages of spatial filtering, by illuminating the grating with slightly incoherent light, e.g., having a small range of wavelengths and angles. A slightly incoherent system provides a trade-off between depth of focus and distortion from coherent artifacts.
Oblique Imaging. A code plate may be illuminated by a collimated, coherent light beam at an angle such that the zero order beam passing through the code plate and the first order diffracted beam have an equal and opposite angle with respect to the direction normal to the plane of the grating, an angle known as the Littrow angle. Under these conditions, a first order beam is also diffracted back, towards the light source. See FIG. 2, which illustrates oblique illumination at the Littrow angle.
The principle of oblique illumination has been used in the integrated circuit industry to extend the resolution of patterns containing repeating features. Because the zero and first order beams are on opposite sides of the vertical, the numerical aperture (NA) of the imaging lens is effective doubled. For a grating that is under coherent illumination perpendicular to the plane of the grating, the smallest period that can be imaged by a lens with a given NA is
                    P        =                              λ                          sin              ⁢                                                          ⁢              θ                                =                      λ            NA                                              (        3        )            But the smallest period that can be imaged by a lens illuminated at the Littrow angle is
                    P        =                  λ                      2            ⁢                                                  ⁢            NA                                              (        4        )            
Oblique illumination of gratings thus produces a high effective depth of focus. Oblique illumination allows one to image in air, vacuum, or other media gratings whose periods approach half the wavelength of the imaging light in the particular medium. Oblique illumination has the disadvantage that the contrast of the fringes is somewhat limited by the diffraction efficiency of the grating. Also, diffractive artifacts can tend to degrade the fringe pattern.
Other work by the inventors. Other work by the present inventors (alone or in collaboration with others) includes L. Jiang et at. “Portable Coordinate Measuring Tool,” presentation at the 49th International Conference on Electron, Ion and Photon Beam Technology and Nanofabrication, Orlando, Fla. (May 31-Jun. 1, 2005); L. Jiang et al., “Technique for Separately Viewing Multiple Levels,” presentation at the 48th International Conference on Electron, Ion and Photon Beam Technology and Nanofabrication, San Diego, Calif. (Jun. 1-4, 2004); L. Jiang et al., “Technique for Separately Viewing Multiple Levels,” J. Vac. Sci. Technol. B, vol. 22, pp. 3405 ff (2004); L. Jiang et al., “Portable coordinate measuring tool,” J. Vac. Sci. Technol. B, vol. 23, pp. 3056 ff (2005); M. Feldman et al., “Method of Patterning Two Patterns on a Single Transparent Substrate to Allow the Patterns to be Viewed Independently,” U.S. provisional patent application 60/578,577, filed Jun. 10, 2004; and D. L. White et al., “The interference fringe aligner,” J. Vac. Sci. & Technol. B, vol. 6, pp. 1921-1924 (1988).